MÜNCHENER STOCHASTIK-TAGE 1998

The quantitative treatment of the statistical uncertainties inherent in the material and geometrical properties of structures and mechanical components as well as the loading conditions to which they are expected to be exposed during their design life, allows the estimation of their reliability. In this context the developments of both efficient and accurate methods receive considerable attention. It basically requires the solution of a multi-dimensional integral over the failure domain confined by a so-called limit state function g(X)=0, where the vector X contains all the uncertainties, as modeled by random variables. The methods of solution maybe categorised in approximate and accurate procedures respectively. The first type is based on a linear approximation of the limit state function at the so-called design point (point of maximum likelihood), also denoted as the reliability method of first order - and its further development to the second order, which implies the consideration of the curvature at the linearization point (second order reliability methods). The accurate procedures encompass either numerical integration of Monte Carlo simulation (MCS) respectively.

In this presentation some important aspects of the properties of the procedures will be discussed. This applies particularly to the fact that in most cases the limit state function is available only pointwise - as obtained from structural (e.g. FE) analysis - rather than in analytical form. For those cases the determination of the design point(s) by optimization procedures may cause severe difficulties. The improvement of the procedures also applies to expanding the dimensionality, i.e. the number of random variables to be treated.

The second part of the lecture concentrates on the optimization of structures and mechanical components based on reliability considerations. This implies the consideration of the consequences in terms of total and partial failure (damage) respectively as well as maintenance, the cost of which in context with their probability of occurrence should be a minimum. So far the more recently suggested approaches for reliability based optimization are formulated such that the decision criteria are mostly introduced as constrained single objective functions focusing on the minimization of structural weight, total life time costs, etc. while observing reliability constraints (i.e. target reliability). It is shown that, at this stage, multi-objective problem formulations are still restricted to smaller types of systems.

Zur Eröffnung der Tagung
Zum Tagungsprogramm
Zur Programmübersicht
Zur Homepage der Münchener Stochastik-Tage 1998

März 1998: Prof. Dr. Marti, LRT/WE1

Web Design by Mounir Chahine